What Is Applied Mathematics?

Applied mathematics is the mathematics that is created in response to problems in science, engineering, and society. Applied mathematicians work on a wide variety of topics, constructing methods for multi-criteria decision making (i.e., decisions that must take multiple conflicting criteria into consideration, requiring discrete mathematics and statistics), predicting how the financial markets will behave (requiring probability/statistics, analysis, optimization), or analyzing how fluid flows around solids (requiring expertise in computational methods and analysis). Students with an applied mathematics background are prepared for a wide variety of careers in technology, finance, insurance, manufacturing, logistics, pharmaceuticals, and more.

Our graduates work in financial and insurance companies as analysts, computer companies as programmers and hardware developers, and in many different fields as researchers, as well as academia. They have gone to excellent graduate schools in mathematics (pure, applied, or financial), physics, design, accounting, and M.B.A. programs.

Why Illinois Tech?

We are particularly strong in contemporary topics in applied mathematics. Our students develop their skills in logic and abstraction as in any mathematics program, but they also learn advanced tools for analyzing modern problems, from areas including:

We offer a wide variety of courses. Our students have ample opportunity to assemble a portfolio of courses that will satisfy both intellectual needs and career preparation. Our courses cover classic applied mathematics as well as contemporary applied topics, attracting students majoring in applied mathematics but also students from across the university.

We have flexible programs:

A student can choose a specialization (such as in mathematical finance or statistics) if desired.

Each student picks a minor, which consists of five related courses in an area outside of mathematics. This gives students enough background to understand what it takes to be able to apply mathematics appropriately in another field. With a minor in computer science, business, or one of the engineering areas, for example, the student will be well prepared to enter the job market in business or government.

Students often participate in research projects, whether as part of a course or with faculty and graduate students over the summer. Others do internships. There is funding available to support select undergraduate students doing research.

Other attractions for students:

Personal attention and small class size

A weekly departmental colloquium featuring experts from all over the world

Several research seminars in which students and faculty discuss their latest research

The IIT SIAM (Society for Industrial and Applied Mathematics) and IIT AWM (Association for Women in Mathematics) student chapters, which give students the opportunity to explore intriguing aspects of mathematics, participate in mathematics competitions, be mentored by women in mathematics, and more.

The world-class city of Chicago.

Careers

Applied mathematics at Illinois Tech is challenging. When you finish the program, you will discover that many different options await you. Although many positions with the title “mathematician” or “statistician” require a graduate degree, there is a growing demand for people whose undergraduate training emphasizes modern applied mathematics. These positions are typically interdisciplinary and focus on a combination of modeling, analysis, statistics, and computation. You will find applied mathematicians in such diverse fields as actuarial science, education, financial services, pharmaceuticals research, and municipal administration. Applied mathematicians are found everywhere in commerce, industry, and government where quantitative methods are used to make decisions. Our graduates have gone on to top graduate schools for further study, and found positions at places like Goldman Sachs, Blue Cross Blue Shield, Wolfram (developers of Mathematica), and more.

Research

With Ph.Ds. from Massachusetts Institute of Technology, UCLA, Cornell, New York University, Georgia Tech, University of Minnesota, University of California San Diego, University of Illinois at Urbana-Champaign, Vanderbilt, and Illinois Tech, to name a few, our applied mathematics faculty are pushing the boundaries of what we know in many areas, including applied analysis, computational mathematics, discrete applied mathematics, stochastics and mathematical finance, and statistics.

The applied analysis research group studies mathematical problems arising from physical, chemical, geophysical, biophysical, and materials sciences, often described by time-dependent partial, ordinary, or integral differential equations, together with sophisticated boundary conditions, interface conditions, and external forcing.

The computational mathematics research group designs and analyzes numerical algorithms and answers fundamental questions about the underlying physics. They construct and analyze algorithms for approximating functions and integration in high dimensions, develop accurate mathematical models and efficient numerical methods to investigate dynamics of interfaces, and establish analytical and computational techniques for extracting effective dynamics from multiscale phenomena that are abundant in geophysical and biophysical systems.

The discrete mathematics group studies theoretical, algorithmic, and computational problems in the fields of graph theory, discrete optimization, combinatorics, and algebraic geometry, such as network science, combinatorial search, and computational algebra, with applications in biology, computer science, physics, management sciences, and engineering.

The research outcome of the stochastics group provides modeling tools for analysis, control, and numerical study of various stochastic systems that evolve in time and space, and are subject to randomness, including the structured dependence between stochastic processes, random sequence comparison, stochastic partial differential equations and stochastic dynamical systems. Our research in the area of mathematical finance provides quantitative models of financial securities that allow pricing, hedging, and mitigating the risk of complex financial products.

The statistics research group works on applied problems in several areas of statistics from the theoretical, methodological, and computational points of view, such as design and analysis of experiments with complex structures, Monte Carlo methods, algebraic statistics, statistical network modeling and uncertainty quantification, and Bayesian statistics, with close collaboration with scientists and engineers from mechanical, manufacturing, civil, and transportation engineering, social sciences, biology, neuroscience, business, and management.